Certifiable function

An integer-valued function $f$ is $g$-certifiable when every input $x$ with $f(x)=k$ has a set of at most $g(k)$ coordinates whose values alone guarantee that $f\ge k$.

Talagrand's product-space inequality gives sub-Gaussian-type concentration for a bounded-differences, certifiable function, with a variance scale controlled by the certificate size.

The entropy method combines a coordinatewise certificate with tensorization of entropy to bound the moment-generating function of a certifiable random quantity and hence its tails.